Kinetics of the ethylene trimerization reaction on a homogeneous chromium-pyrrole catalyst

Article abstract of DOI:10.1134/S0965544112050131

The results of studying the kinetics of the reaction of ethylene trimerization under the action of a homogeneous chromium-pyrrole catalyst have been presented. It has been shown that the reaction order with respect to ethylene decreases from 1.4 to a value close to 1 within 15 min after the start of the reaction, which is explained by the presence of two types of catalytic centers that catalyze the reactions of the first and second order with respect to ethylene. A model that includes the degradation of the second type of the catalyst during the reaction and inhibition of the activity of the first-type catalyst by the products has been proposed. Pleiades Publishing, Ltd., 2012.

Full text of DOI:10.1134/S0965544112050131

ISSN 0965ꢀ5441, Petroleum Chemistry, 2012, Vol. 52, No. 5, pp. 335–340. © Pleiades Publishing, Ltd., 2012.
Original Russian Text © T.M. Zilbershtein, V.A. Kardash, M.V. Lipskikh, V.V. Suvorova, A.K. Golovko, 2012, published in Neftekhimiya, 2012, Vol. 52, No. 5, pp. 371–376.
Kinetics of the Ethylene Trimerization Reaction on a Homogeneous
Chromium–Pyrrole Catalyst
T. M. Zilbershteina, V. A. Kardasha, M. V. Lipskikha, V. V. Suvorovaa, and A. K. Golovkob
a OOO NIOST, Kuzovlevskii trakt 2, Tomsk, 634067 Russia
eꢀmail: ztm@niost.ru
b Institute of Petroleum Chemistry, Siberian Branch, Russian Academy of Sciences,
Akademicheskii pr. 3, Tomsk, 634055 Russia
Received April 09, 2012
Abstract—The results of studying the kinetics of the reaction of ethylene trimerization under the action of a
homogeneous chromium–pyrrole catalyst have been presented. It has been shown that the reaction order
with respect to ethylene decreases from 1.4 to a value close to 1 within 15 min after the start of the reaction,
which is explained by the presence of two types of catalytic centers that catalyze the reactions of the first and
second order with respect to ethylene. A model that includes the degradation of the second type of the catalyst
during the reaction and inhibition of the activity of the firstꢀtype catalyst by the products has been proposed.
DOI: 10.1134/S0965544112050131
The reaction of ethylene trimerization over chroꢀ containing cocatalyst diethylaluminum chloride
(DEAC) [8].
mium catalysts was discovered in 1967 during the
research work at the Phillips Petroleum company as a
side reaction during the polymerization of ethylene.
Although these results were patented in 1967 [1], they
were published in the scientific literature much later,
in 1977 [2]. Even at that time it was pointed out that
the dependence of the reaction rate is second order in
ethylene pressure, but detailed studies of the reaction
kinetics were not carried out. There are several papers
concerning a detailed study of kinetic relationships, in
which the kinetic features of ethylene oligomerization
on an arylꢀcyclopentadienylꢀtitanium catalyst [3] or a
CrꢀPNPNHꢀcatalyst [4] and the related reaction of
ethylene tetramerization on a CrꢀPNP catalyst were
investigated [5, 6]. It was shown that the dependence
of the reaction rate on ethylene pressure on various
catalysts can be of both the first and second order. An
intermediate order of the reaction indicating the comꢀ
plexity of its mechanism is also possible [5, 6].
Researchers have succeeded in synthesizing a series
of chromiumꢀbased catalytic complexes that do not
require additional activation and are similar in comꢀ
position to the Phillips catalyst. It was found that
chromium is in the formal oxidation state +1 in these
complexes [9], as was confirmed by the ESR spectra of
solutions of the chromium catalysts [10]. However, the
catalytic activity of these compounds in the reaction of
ethylene trimerization is relatively low compared with
the known catalysts of a nonꢀstoichiometric composiꢀ
tion.
The purpose of this work is to study the kinetic
dependences of the reaction of ethylene trimerization
under the action of a modified chromium–pyrrole
catalyst system prepared using microwave irradiation,
because it has a much greater activity in comparison
with known analogues owing to changes in the comꢀ
position and the catalyst preparation procedure [11].
Most of the trimerization catalysts described to
date do not possess precisely determined structure.
They were prepared by mixing several components—
a transition metal (usually chromium) compound, a
ligand and an activator (organometallic compound)
[7]. In this regard, the properties of the formed cataꢀ
lysts depend strongly on the ratio of the components
and the method of preparation. In some cases, modiꢀ
fiers of the catalytic activity, such as halogenated comꢀ
pounds, are added. Thus, the Phillips catalyst system
used in the industry is prepared from chromium(III)
EXPERIMENTAL
The solvents were dried by refluxing over sodium
metal followed by distillation over sodium hydride. To
prepare the catalyst, a 1.0 M DEAC solution in hexane
and a 1.9 M TEA solution in toluene were used. The
reagent 2,5ꢀdimethylpyrrole of 98% purity was used
without further purification. Anhydrous chroꢀ
mium(III) ethylhexanoate was prepared according to
a known procedure [12] with additional drying in a
vacuum of 200 Pa at 200
°С.
ethylhexanoate (Cr(EH)3),
2,5ꢀdimethylpyrrole
The microwave irradiation of solutions of orgaꢀ
(DMP), triethylaluminum (TEA), and the halogenꢀ noaluminum compounds (OACs) was conducted in a
335

336
ZILBERSHTEIN et al.
(b)
Ethylene uptake, g
(а)
Ethylene uptake, g
30
25
20
15
10
5
P = 0.8 MPa
4
40
35
30
25
20
15
10
5
T = 50°C
1
2
P
P
P
P
= 0.4 MPa
= 0.6 MPa
= 1.0 MPa
= 1.6 MPa
30°C
40°C
50°C
60°C
70°C
1
2
3
4
5
3
3
4
4
5
2
1
3
2
1
0
5
10 15 20 25 30
Time, min
0
5
10 15 20 25 30
Time, min
Fig. 1. The dependence of the amount of ethylene consumed on the (a) ethylene pressure and (b) reaction temperature.
MARSꢀ5 microwave oven, manufactured by CEM, in pressure in the reactor was released and the reaction
the continuous mode at a rated power of 400 W.
mixture was discharged through the bottom valve. The
reaction mixture and the sample taken 15 min after the
start of the reaction were analyzed by gas chromatogꢀ
raphy.
The quantity of ethylene consumed during the
reaction was determined by direct measurement of the
ethylene flow rate with a mass flowmeter.
All catalyst samples prepared using microwave
treatment were tested in the ethylene trimerization
reaction run in a special setup included a highꢀpresꢀ
sure reactor of 0.5 L capacity equipped with pressure
and temperature sensors, an oilꢀfilled cooling jacket
connected to a thermostat, and feed lines for dosage of
ethylene, hydrogen, and solvent (cyclohexane). Ethylꢀ
ene was fed into the reactor through a tube, lowered to
the lower part of the reactor under a layer of a solvent.
Cyclohexane was dosed using a membrane metering
pump, the amount of the solvent dose was determined
by a mass flow meter. The setup was equipped with a
computerꢀrun process control system, which made it
possible to record sensor readings and to control the
reactor temperature, the feed lines, etc.
RESULTS AND DISCUSSION
To study the kinetic characteristics of the reaction,
experiments with varying both temperature (from 30
to 70
sure (in the range from 0.4 to 1.6 MPa during the reacꢀ
tion at 50 ) were carried out.
°С at a pressure of 0.8 MPa) and ethylene presꢀ
°C
The curves of the dependence of ethylene conꢀ
sumption during the reaction on the temperature
(Fig. 1a) and pressure (Fig. 1b) tend to deviate from
linearity: during the first minutes of the reaction there
is an increased consumption of ethylene, which then
decreases and finally becomes almost linear with a
slight decrease during the further course of the reacꢀ
tion. Such a deviation from linearity leads to inaccuraꢀ
cies when using the averaged values of the reaction rate
for 30 min in the kinetic calculations and requires
more detailed consideration.
During the reaction, hexeneꢀ1; С4, С8, and С10
olefins; and heavier products are formed. The selectivꢀ
ity of the reaction for hexeneꢀ1 is about 90%; so, for
simplifying further calculations, the transformation of
ethylene to higher olefins can be considered one reacꢀ
tion leading to a mixture of products.
The catalyst solution was prepared by a previously
developed method [11] using the ratio of reactants
Cr(EH)3/DMP/TEA/DEAC = 1 : 5 : 36 : 14.
Ethylene Trimerization Reaction
The reactor was charged with 160 g of cyclohexane,
the solvent was saturated with hydrogen under presꢀ
sure of 100 kPa, then the reactor was heated to the
desired temperature. The catalyst solution (2.0 mL,
0.8 mg Cr) was injected through the valve with a
syringe under hydrogen counter flow. The feed of ethꢀ
ylene was open to achieve a specified pressure. During
the reaction, the desired temperature was maintained
using thermostat, and the desired pressure was mainꢀ
tained by pumping in ethylene as it was consumed.
A sample (1–2 mL) was withdrawn through the
From the literature it is known that Cr(I) comꢀ
bottom valve 15 min after the beginning of ethylene plexes are active catalysts for trimerization [9]. It can
supply. After 30 min, the ethylene feed was stopped be assumed that the formed catalyst of an undeterꢀ
and reactor cooling was switched on. After 5 min, the mined composition preferably contains Cr(I) in the
PETROLEUM CHEMISTRY Vol. 52
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2012

KINETICS OF THE ETHYLENE TRIMERIZATION REACTION
337
y = 1.396
x
– 1.722
1–5 min
ln
U
R2 = 0.969
2.0
1.5
1.0
0.5
0
y = 1.115
x
– 1.348
5–10 min
10–15 min
15–20 min
R2 = 0.980
y = 0.954
x
– 1.325
R2 = 0.967
y = 0.863
x
– 1.290
R2 = 0.876
–0.5
1.0
1.5
2.0
2.5
3.0
ln
P
Fig. 2. Determination of the reaction order with respect to ethylene.
form of two basic types of particles that are active as
ethylene trimerization catalysts.
A decrease in the reaction order with time indicates
that the rate of the secondꢀorder reaction with respect
to ethylene decreases rapidly during the reaction, and
after 10–15 min the reaction rate is completely deterꢀ
mined by the reaction of the first order in ethylene.
Apparently, the second catalyst species is unstable and
rapidly decays during the course of the reaction.
The trimerization reaction is believed to occur by
the mechanism proposed by Briggs [13]. The differꢀ
ence in the formal order between the two trimerization
reactions can be explained by the fact that only one
ethylene molecule is involved in the rateꢀlimiting step
for reaction 1 and two molecules for reaction 2. In the
latter case, it is possible only in the stage of the coordiꢀ
nation of first two ethylene molecules to a free active
catalyst particle. In the former case, there are two
options: the rateꢀlimiting step may be coordination of
the third ethylene molecule to the chromiumꢀcycloꢀ
pentane intermediate with the subsequent formation
of chromiumꢀcycloheptane, or stepwise coordination
of the first or second molecule of ethylene. Theoretical
calculations for the Phillips trimerization catalyst
indicated that the formation of chromiumꢀcyclohepꢀ
tane is the rateꢀdetermining step [14].
In view of the aforementioned nonlinearity of the
ethylene consumption curves, average rates of ethylꢀ
ene consumption in the intervals 1–5, 5–10, 10–15,
and 15–20 min are considered. Shorter intervals lead
to the appearance of inaccuracies due to cyclic fluctuꢀ
ations in the ethylene feed rate, which account for ca.
10% of the mean value and are caused by fluctuations
in the temperature of the reaction mixture and the gas
phase in the reactor within 2–3 degrees.
Figure 2 shows plots of the dependence of the averꢀ
age ethylene consumption rate on the pressure р in the
logarithmic coordinates. The linearization of the
curves for each of the above intervals makes it possible
to determine the formal order of the reaction with
respect to ethylene for each of the intervals. Thus, in
the range of 1–5 min the reaction order is 1.40; then it
decreases to 1.11 in the range of 5–10 min and to 0.95
in the range of 10–15 min. In the interval of 15–
20 min, an additional decrease in the formal reaction
order to 0.86 is observed. However, this is largely due
to the deviation of the dependence from the linear
form in these coordinates, primarily because of the
rapid decrease in activity in this interval at 1.6 MPa.
Without taking into account this deviation, the formal
reaction order in this case is also close to unity. Thus,
the first order of the reaction with respect to ethylene
in general is observed after 10 min of the reaction and
a mixed order at reaction times shorter than 10 min.
The mixed order usually indicates the occurrence of
two parallel reactions, of which one has a lower (first)
and the other has a higher (second) order in a compoꢀ
nent. We assume that the reactions of trimerization
and oligomerization of ethylene are parallel reactions.
The oligomerization reaction leads to the formation of
significant amounts of buteneꢀ1 as a byproduct during
the first minutes of the reaction (Table 1).
A similar case of two catalytic cycles for a homogeꢀ
neous chromium catalyst in the ethylene tetramerizaꢀ
tion reaction is described in the literature [6]. The
authors suggest that two types of catalysts in this case
may be isomers, one of which leads to the formation of
only hexeneꢀ1 and coꢀtrimerization products during
Table 1. Quantity of buteneꢀ1 and hexeneꢀ1 in the course of
the trimerization reaction. Reaction conditions: 50
°
C; ethꢀ
ylene, 0.4 MPa
Time, min
2
5
10
15
30
Buteneꢀ1, g
0.14
0.37
2.31
0.49
4.44
0.37
6.15
0.43
Hexeneꢀ1, g 0.84
11.01
PETROLEUM CHEMISTRY Vol. 52
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2012

338
exp(–Ea(1)/RT) [C H ]/ –1
ZILBERSHTEIN et al.
is based on the results of our studies and published data
A
υ
j
2 4
[15], confirming that the reaction of ethylene trimerꢀ
ization in neat hexeneꢀ1 proceeds much slower than in
the case of using cyclohexane as a solvent.
y
= 2.29e – 5.28e
– 4
– 4
0.25
0.20
0.15
0.10
0.05
0
2
R
= 0.956
For simplicity, assume that all olefinic products
compete with ethylene in the interaction with the catꢀ
alyst with an overall constant Ki. For reaction 2 occurꢀ
ring during first few minutes, make an assumption on
the degradation of the catalyst during the reaction. For
competitive inhibition of the catalyst 1 by reaction
products, the following relations are correct:
[Cr1 * olefin]
Ki = ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ,
(3)
[Cr1][olefins]
1.0
2.0
3.0
4.0
[
Cr1]0 = [Cr1] + [Cr1 ethylene] + [Cr1
*
*
olefin], (4)
3
3
[
olefins], 10 mol/m
–0.05
where [Cr1]0 is the initial concentration of the catalyst
Fig. 3. Example of determination of Ki for the reaction at
of reaction 1, [Cr1] is the current concentration of free
catalyst 1, [Cr1 *ethylene] is the total concentration of
chromium in the form of intermediates in the catalytic
cycle of ethylene trimerization, [[Cr1 *olefin] is the
total concentration of chromium in the form of comꢀ
plexes with alphaꢀolefins.
Assuming that reaction 1 proceeds rapidly, and the
proportion of intermediates [Cr1 *ethylene] is very
small, expression (4) can be simplified to
45°C.
the entire course of the reaction, and the second, in
addition, promotes the formation of significant
amounts of buteneꢀ1 at the beginning of the reaction.
To determine the activation energy and the preꢀ
exponential factor in the Arrhenius equation, the temꢀ
perature dependence of the reaction rate was studied.
For the firstꢀorder reaction with respect to ethylene
(reaction 1), the temperature dependence in the interꢀ
val from 15 to 20 min at an ethylene pressure of 0.8
MPa was investigated. Using the approximate assumpꢀ
tion that the rate of reaction 1 remains stable from 1 to
20 min, the average rates of the secondꢀorder reaction
(reaction 2) in the range from 1 to 5 min for temperaꢀ
[Cr1]0 = [Cr1] + [Cr1
*
olefin].
(5)
Then, with allowance for Eq. (3), we obtain a corꢀ
rected expression for the rate of reaction 1:
A1
–Ea(1)/RT
d[olefins]
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ = ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀe
[C2H4]. (6)
dt
1 + Ki[olefins]
tures from 30 to 65°С can be calculated by subtracting
the calculated rate of reaction 1 from the actual averꢀ
age reaction rate.
Let us assume that the degradation reaction of catꢀ
alyst 2 is first order with respect to the catalyst:
Rate equations for reactions 1 and 2 are as follows:
d[Cr2]
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ = kCr [Cr2].
(7)
2
–Ea(1)/RT
dt
d[olefins]
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ = A1e
[C2H4],
(1)
(2)
dt
Assume that the rate of reactions 1 and 2 is proporꢀ
tional to the concentration of the active form of the
catalyst:
–Ea(2)/RT
2
d[olefins]
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ = A2e
[C2H4] ,
dt
where [olefins] stands for the total concentration of
olefinic products (hexeneꢀ1, buteneꢀ1, octeneꢀ1,
decenes, etc.), expressed in moles of ethylene conꢀ
verted per unit volume.
'
A1= [Cr1] ,
(8)
A1
A2
=
'
[Cr2].
(9)
A2
The study of the ethylene consumption plots
(Figs. 1a, 1b) shows that a decrease in the reaction rate
occurs in the initial reaction period (ca. 5 min). Then,
the rate remains almost constant or, in most cases,
there is a further slow decrease. Since it was previously
found that the rate of the reaction 15 min after it
beginning is determined mainly by (firstꢀorder) reacꢀ
tion 1, we assume that at constant catalyst and ethylꢀ
ene concentrations the slowdown of the reaction is due
to reversible inhibition of the catalyst by the reaction
Integrating Eq. (7) over the interval from 0 to
t
and
from the initial concentrations Cr2 0
[
] to the actual
value [Cr2] at a time
t
, we obtain the corrected expresꢀ
sion for reaction 2:
–kCr
t
–Ea(2)/RT
2
d[olefins]
2
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ = A2e
e
[C2H4] .
(10)
dt
Summing Eqs. (6) and (10), multiplying both sides
products hexeneꢀ1 and other olefins. This assumption by dt and (1 + Ki), we obtain:
PETROLEUM CHEMISTRY Vol. 52
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2012

KINETICS OF THE ETHYLENE TRIMERIZATION REACTION
339
Table 2. Coefficients i and Cr2 at various temperatures
K
k
d[olefins](1 + Ki[olefins])
–4
3
–4 –1
–kCr
t
Temperature,
°
C
K
i, 10 m /mol
k
, 10
s
–Ea(2)/RT
2
Cr2
2
=
(A2e
e
[C2H4] (1 + Ki[олефины])
(11)
30
40
45
60
70
2.1
2.6
2.3
2.0
1.9
10.7
14.5
15
+
A1e–Ea(1)/RT[C2H4])dt.
Since the rate of reaction 2 15–20 min after the
18
beginning of the reaction greatly decreases, it can be
neglected. In this case, Eq. (11) takes the following
form:
95
d[olefins](1 + Ki[olefins])
the solubility in cyclohexane, we obtain the following
correction factor for the mass of the consumed ethꢀ
ylene to calculate the concentration of olefinic prodꢀ
(12)
A1e–Ea(1)/RT[C2H4]dt.
s
=
Taking the reaction rate = d/dt, we obtain an ucts in the reaction mixture:
v
expression for calculating Ki from experimental data
on the reaction rate and concentration of the olefins
20 min after the reaction:
[olefins]M
ρol
s = 1 + ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ.
(14)
A1e–Ea(1)/RT[C2H4]
v
Here,
М
= 0.028 kg/mol, ρол = 690 kg/m3.
Ki[olefins] = ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ – 1.
(13)
The final expression for the rate of the formation of
olefins can be written as follows:
It is preferable to determine Ki from the experiꢀ
mental data by plotting the dependence of the rightꢀ
hand side of Eq. (13) on the concentration of olefinic
products and calculating the sought quantity from the
slope of the linear approximation of the resulting
graph. An example of such a determination for a temꢀ
–kCr
t
–Ea(2)/RT
2
d[olefins]
2
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ = A2e
e
[C2H4]
dt
(15)
A1
+
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀe–Ea(1)/RT[C2H4].
1 + Ki[olefins]
perature of 45
°
С is shown in Fig. 3.
The uptake of ethylene, in addition to its transforꢀ
Taking the rate of the formation of olefins to be
mation to olefinic products, is also caused by its dissoꢀ constant in small (10 s) time intervals, it is possible to
lution in the products. Taking the solubility of ethylene numerically integrate Eq. (15), and with allowance for
in the reaction products to be approximately equal to the correction to determine from Eq. (14) the estiꢀ
P
= 1.6 MPa, Ethylene uptake, g
1
P
2
P
= 0.4 MPa
,
T
= 50°C
= 50°C (calculation
= 50°C
= 50°C (calculation
= 30°C
= 30°C (calculation
= 65°C
= 65°C (calculation
= 50°C
= 50°C (calculation
45
40
35
30
25
20
15
10
5
= 0.4 MPa
,
T
)
)
)
)
)
5
P
= 1.0 MPa, T
P
3
= 1.0 MPa, T
P
= 0.8 MPa, T
P
4
= 0.8 MPa, T
2
4
P
= 0.8 MPa
,
T
P
= 0.8 MPa
,
T
3
5 P = 1.6 MPa
= 1.6 MPa
,
T
P
,
T
1
20
0
5
10
15
25
30
Time, min
Fig. 4. Comparison of experimental and calculated ethylene uptake curves.
PETROLEUM CHEMISTRY Vol. 52 No. 5 2012

340
ZILBERSHTEIN et al.
mated quantity of ethylene consumed at a given time
of the reaction.
The constant kCr2 was determined numerically by
comparing the experimental and calculated curves
using the least squares method; the results are shown
in Table 2.
ACKNOWLEDGMENTS
The authors thank ZAO Sibur Holding for financꢀ
ing the work and permission to publish.
REFERENCES
At a temperature of 70°С and higher, the rate of the
1. R. M. Manyik, W. E. Walker, and T. P. Wilson, US
Patent No. 3300458 (1967).
degradation of the type 2 catalyst sharply increases. In
this case, the initial jump of ethylene consumption in
the plot of the dependence of ethylene uptake on time
almost disappears (Fig. 16).
2. R. M. Manyik, W. E. Walker, and T. P. Wilson, J. Catal.
47, 197 (1977).
3. H. Hagen, Ind. Eng. Chem. Res. 45, 3544 (2006).
Using the obtained values, it is possible to calculate
the total rate of the formation of olefinic products
under given conditions at any time from the beginning
4. A. Wöhl, W. Müller, S. Peitz, et al., Chem.ꢀEur. J. 16
,
7833 (2010).
of the reaction. Extrapolation to 50
°С
gives values for
5. R. Walsh, D. H. Morgan, A. Bollmann, and J. T. Dixon,
Ki and kCr2 of 2.2
×
10–4 m3/mol and 16
×
10–4 s–1
,
Appl. Catal., A 306, 184 (2006).
respectively. Figure 4 shows a comparison of experiꢀ
mental and calculated curves under various condiꢀ
tions. Good agreement between the model and experꢀ
imental data for most of the reaction conditions conꢀ
firms that the change in ethylene pressure has no effect
on Ki and kCr2. Therefore, this model can be used for
calculations on the reaction course when ethylene
pressure is varied from 0.4 to 1.6 MPa and temperaꢀ
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PETROLEUM CHEMISTRY Vol. 52
No. 5
2012